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Transactions of the American Mathematical Society

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Symmetry of ground states
for a semilinear elliptic system


Author: Henghui Zou
Journal: Trans. Amer. Math. Soc. 352 (2000), 1217-1245
MSC (1991): Primary 35B40, 35J60
DOI: https://doi.org/10.1090/S0002-9947-99-02526-X
Published electronically: September 20, 1999
MathSciNet review: 1675167
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $n\ge 3$ and consider the following system

\begin{equation*}\Delta \mathbf{u}+\mathbf{f}(\mathbf{u})=0,\quad \mathbf{u}>0,\qquad x\in\mathbf{R}^n.\end{equation*}

By using the Alexandrov-Serrin moving plane method, we show that under suitable assumptions every slow decay solution of (I) must be radially symmetric.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-99-02526-X
Received by editor(s): April 4, 1997
Received by editor(s) in revised form: October 20, 1997
Published electronically: September 20, 1999
Additional Notes: Research supported in part by NSF Grants DMS-9418779 and DMS-9622937, an Alabama EPSCoR grant and a faculty research grant of the University of Alabama at Birmingham
Article copyright: © Copyright 1999 American Mathematical Society

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